Duality and Stability for Functional Inequalities
Functional Analysis
2016-09-06 v1
Abstract
We develop a general framework for using duality to "transfer" stability results for a functional inequality to its dual inequality. As an application, we prove a stability bound for the Hardy-Littlewood-Sobolev inequality, which is related by duality, and the results proved here, to a stability inequality for the Sobolev inequality proved by Bianchi and Egnell, and extended by Chen, Frank and Weth. We also discuss how the results proved here can be combined with the proof of functional inequalities by means of flows to prove stability bounds with computable constants
Cite
@article{arxiv.1609.00936,
title = {Duality and Stability for Functional Inequalities},
author = {Eric A. Carlen},
journal= {arXiv preprint arXiv:1609.00936},
year = {2016}
}
Comments
This paper will appear in The Annales de la Faculte des Sciences de Toulouse